We described how methods such as LDA and QDA are not meant to be used with many predictors \(p\) because the number of parameters that we need to estimate becomes too large.
For example, with the digits example \(p=784\), we would have over 600,000 parameters with LDA, and we would multiply that by the number of classes for QDA.
Kernel methods such as kNN or local regression do not have model parameters to estimate.
However, they also face a challenge when multiple predictors are used due to what is referred to as the curse of dimensionality.